Network synthesis design of microwave acoustic wave filters

ABSTRACT

A multi-band acoustic wave microwave filter, including a signal transmission path having an input and an output; a plurality of nodes disposed along the signal transmission path; a plurality of non-resonant branches respectively coupling one or more nodes to ground, wherein each non-resonant branch comprises at least one non-resonant element; and a plurality of resonant branches that couple one or more nodes to ground and include a plurality of resonators on said branches, wherein the plurality of resonators define a first band and at least one additional band and further wherein the difference between the lowest resonant frequency and the highest resonant frequency of the first band is at least 1.25 times the average separation of the resonators.

RELATED APPLICATIONS DATA

This application is a continuation of U.S. patent application Ser. No.15/673,916, filed Aug. 10, 2017, which is a continuation of U.S. patentapplication Ser. No. 15/366,620, filed Dec. 1, 2016 (now U.S. Pat. No.9,754,060), which is a continuation of U.S. patent application Ser. No.14/945,736, filed Nov. 19, 2015 (now U.S. Pat. No. 9,524,360), which isa continuation of U.S. patent application Ser. No. 14/666,100, filedMar. 23, 2015 (now U.S. Pat. No. 9,208,274), which is acontinuation-in-part of U.S. patent application Ser. No. 14/214,562,filed Mar. 14, 2014 (now U.S. Pat. No. 8,990,742), which is acontinuation-in-part of U.S. patent application Ser. No. 13/838,943,filed Mar. 15, 2013 (now U.S. Pat. No. 9,038,005), which applicationsare all expressly incorporated herein by reference in their entireties.

FIELD OF THE INVENTION

The present inventions generally relate to microwave filters, and moreparticularly, to acoustic wave microwave filters.

BACKGROUND OF THE INVENTION

Low loss, frequency selective electrical signal filters forcommunications applications were developed beginning around 1910, fortelegraphy and telephony uses, particularly for multiplexing andde-multiplexing of communication signal channels carried on longdistance cables and wireless links. Filter design methods, named “image”or “image parameter” design methods, were developed by BellLaboratories, among others (see George A. Campbell, “Physical Theory ofthe Electric Wave Filter”, The Bell System Technical Journal, Volume I,No. 2 (November 1922); Otto J. Zobel, “Theory and Design of Uniform andComposite Electric Wave-Filters”, The Bell System Technical Journal,Volume II, No. 1 (January 1923)). These filter circuits utilized circuitelements, including inductors, capacitors, and transformers.

In the 1920s, Acoustic Wave (AW) resonators, specifically quartz bulkacoustic wave (BAW) resonators, began to be used in some electricalsignal filters. The equivalent circuit of an AW resonator has tworesonances closely spaced in frequency called the “resonance” frequencyand the “anti-resonance” frequency (see K. S. Van Dyke, “Piezo-ElectricResonator and its Equivalent Network” Proc. IRE, Vol. 16, 1928, pp.742-764). The image filter design methods were applied to filtercircuits utilizing these quartz resonators, and two AW filter circuittypes resulted: “ladder” and “lattice” AW filter designs (see L.Espenschied, Electrical Wave Filter, U.S. Pat. No. 1,795,204; and W. P.Mason, “Electrical Wave Filters Employing Quartz Crystals as Elements”,The Bell System Technical Journal (1934)).

In the 1920s and 1930s, another approach, which came to be referred toas “network synthesis,” was developed for the design of frequencyselective electrical signal filters for communications applications.This new filter circuit design method was pioneered by Foster andDarlington in the United States (see Ronald M. Foster, “A ReactanceTheorem,” Bell Syst. Tech. J., Vol 3, 1924, pp. 259-267, and S.Darlington, “Synthesis of Reactance 4-poles which produce prescribedinsertion loss characteristics”, J. Math Phys, Vol 18, 1939, pp.257-353) and Cauer in Germany (see W. Cauer, U.S. Pat. No. 1,989,545;1935) among others.

In “network synthesis,” after an initial circuit structure is chosen,which includes circuit element types and the way they areinterconnected, the desired loss-less filter response is translated intoa ratio of complex polynomials in the form of complex frequencydependent circuit response parameters such as scattering parameters,e.g. S21 and S11. The S21 scattering parameter may be represented asfollows:

$\begin{matrix}{{{H(s)} = {\frac{N(s)}{D(s)} = {K\frac{\left( {s - z_{1}} \right)\left( {s - z_{2}} \right)\mspace{14mu} \ldots \mspace{14mu} \left( {s - z_{m - 1}} \right)\left( {s - z_{m}} \right)}{\left( {s - p_{1}} \right)\left( {s - p_{2}} \right)\mspace{14mu} \ldots \mspace{14mu} \left( {s - p_{n - 1}} \right)\left( {s - p_{n}} \right)}}}},} & \lbrack 1\rbrack\end{matrix}$

where N(s) is the numerator polynomial, D(s) is the denominatorpolynomial, the z_(i)'s are the roots (or transmission zeroes) of theequation N(s)=0, the p_(i)'s are the roots (or reflection zeroes) of theequation D(s)=0, m is the number of transmission zeroes, n is the numberof reflection zeroes, and K is a scale factor. (Note: transmissionzeroes are the zeroes of S21 and reflection zeroes are the zeroes ofS11, for the loss-less case. When the small but finite real losses areadded later in the circuit design process these zeroes may become smallbut no longer precisely zero, and correspond to the natural frequencies,resonances, of the final filter.) The filter circuit element values maythen be “synthesized” (calculated) exactly in the loss-less case fromthe ratio of complex polynomials. Neglecting losses, which are keptsmall in practice, the response of the “synthesized” circuit matches thedesired response function.

In the 1950s and 1960s, network synthesis was successfully applied tothe design of microwave filters for communications and otherapplications. These new filters utilize high Q (low loss)electromagnetic resonators and electromagnetic couplings between theseresonators as circuit elements (see George L. Matthaei et al., MicrowaveFilters, Impedance-Matching Networks, and Coupling Structures,McGraw-Hill Book Company, pp. 95-97, 438-440 (1964); and Richard J.Cameron et al., Microwave Filters for Communication Systems:Fundamentals, Design and Applications, Wiley-Interscience (2007).).Network synthesis was also applied to the design of acoustic wavefilters for communications and other applications beginning in the1960's. (See Anatol I. Zverev, Handbook of Filter Synthesis, John Wiley& Sons, pp. 414-498 (1967); and Robert G. Kinsman, Crystal Filters:Design, Manufacture, and Application, John Wiley & Sons, pp. 37-105 and117-155, (1987)). In this work, only the resonance of the acoustic waveresonator is included in the initial circuit structure. Theanti-resonance is treated as a parasitic effect added into the circuitafter the element values of the initial circuit are calculated by thenetwork synthesis method.

Beginning in about 1992, thin film surface acoustic wave (SAW)resonators and thin film BAW resonators were developed and began to beused at microwave frequencies (>500 MHz). AW impedance element filter(IEF) designs, were utilized which is an example of an Espenschied-typeladder acoustic wave filter design (see O. Ikata, et al., “Developmentof Low-Loss Bandpass Filters Using Saw Resonators for PortableTelephones”, 1992 Ultrasonics Symposium, pp. 111-115; and Ken-yaHashimoto, Surface Acoustic Wave Devices in Telecommunications: Modelingand Simulation, Springer (2000), pp. 149-161). Image designed AW IEFbandpass filters in SAW and BAW implementations are often used formicrowave filtering applications in the radio frequency (RF) front endof mobile communications devices. Of most particular importance in themobile communication industry is the frequency range from approximately500-3,500 MHz. In the United States, there are a number of standardbands used for cellular communications. These include Band 2 (1800-1900MHz), Band 4 (1700-2100 MHz), Band 5 (˜800-900 MHz), Band 13 (˜700-800MHz), and Band 17 (˜700-800 MHz); with other bands emerging.

The duplexer, a specialized kind of filter, is a key component in thefront end of mobile devices. Modern mobile communications devicestransmit and receive at the same time (using Code Division MultipleAccess (CDMA), Wide-Band Code Division Multiple Access (WCDMA), or LongTerm Evolution (LTE)) and use the same antenna. The duplexer separatesthe transmit signal, which can be up to 0.5 Watt power, from the receivesignal, which can be as low as a pico-Watt. The transmit and receivesignals are modulated on carriers at different frequencies allowing theduplexer to select them; even so the duplexer must provide low insertionloss, high selectively, small circuit area, high power handling, highlinearity, and low cost. The image designed bandpass AW IEF filter isuniversally preferred to be used in a duplexer, because it satisfiesthese requirements, and significantly better than alternatives like thetapped delay line (since it has higher loss), and the resonantsingle-phase unidirectional transducer (SPUDT) filter (since the narrowlines required prevent scaling to microwave frequencies); although thedouble-mode SAW (DMS) (also called longitudinally coupled resonator(LCR)) filter is sometimes used for the receive filter in a duplexer dueto the balanced output it provides and improved rejection. (See DavidMorgan, Surface Acoustic Wave Filters With Applications to ElectronicCommunications and Signal Processing, pp. 335-339, 352-354 (2007)).

Minor variations to these traditional AW IEF filter designs have alsobeen considered for these applications (see, for example, U.S. Pat. No.8,026,776 and U.S. Pat. No. 8,063,717), which typically add one or morecircuit elements (e.g. capacitor, inductor, or AW resonator) to the IEFdesign to enhance or add a particular circuit feature. This can beaccomplished when the influences to the AW IEF circuit are minor enoughthat currently used computer optimization tools converge and produce animproved design after the additional element(s) are added, as comparedto the optimized IEF. This is a stringent requirement for any circuitcontaining AW resonators, with their closely spaced resonances andanti-resonances, and thus permits only very minor variations to thebasic AW IEF design and function.

There is a need for improved microwave acoustic wave filters to provideimproved performance, smaller size, and lower cost; as well as toincorporate tunability. Network synthesis offers a path when thecompound nature of the acoustic wave resonator is incorporated directlyinto the network synthesis process—the subject of this invention.

SUMMARY OF THE INVENTION

In accordance with the present inventions, a method of designing anacoustic microwave filter in accordance with frequency responserequirements (e.g., one or more of a frequency dependent return loss,insertion loss, rejection, and linearity or a passband (e.g., in500-3500 MHz range) and a stop band) is provided. The method comprisesselecting an initial filter circuit structure including a plurality ofcircuit elements comprising at least one resonant element (e.g., aparallel L-C resonator combination of a capacitor and an inductor) andat least one other reactive circuit element (e.g., a capacitor). Theinitial filter circuit structure can be, e.g., an in-linenon-resonant-node circuit structure.

An optional method further comprises selecting the structural type ofeach of the resonant element(s) from one of a surface acoustic wave(SAW) resonator, a bulk acoustic wave (BAW) resonator, a film bulkacoustic resonator (FBAR), and a microelectromechanical system (MEMS)resonator. Another optional method further comprises mapping thefrequency response requirements to a normalized design space, in whichcase, the circuit element values are normalized values that aredetermined based on the mapped frequency response requirements, andunmapping the normalized circuit element values of the acoustic filtercircuit design to a real design space.

The method further comprises selecting circuit response variables (whichmay be lossy or lossless) based on the frequency response requirements(e.g., in the form of a ratio between numerator polynomials definingtransmission zeroes and denominator polynomials defining reflectionzeroes multiplied by a scale factor), and selecting a value for each ofthe circuit elements based on the selected circuit response variables tocreate an initial filter circuit design.

The method further comprises transforming the resonant element(s) andthe other reactive circuit element(s) of the initial filter circuitdesign into at least one acoustic resonator model to create an acousticfilter circuit design. In one embodiment, the acoustic resonator modelis a Butterworth-Van Dyke (BVD) model. In this case, the other reactivecircuit element(s) may comprise an in-shunt admittance inverter inseries with the in-shunt parallel L-C-resonator combination, and anin-shunt non-resonant susceptance in parallel with the in-shunt parallelL-C resonator combination, and the in-shunt parallel L-C resonatorcombination, in-shunt admittance inverter, and in-shunt non-resonantsusceptance may be transformed into one of the BVD model(s). Forexample, the in-shunt parallel L-C resonator combination and thein-shunt admittance inverter may be transformed into an in-shunt seriesL-C resonator combination, and the in-shunt series L-C resonatorcombination and in-shunt non-resonant susceptance may be transformedinto the one BVD model. In this case, the one BVD model may be anin-shunt BVD model. In this embodiment, the reactive circuit element mayfurther comprise two in-line admittance inverters coupled to a nodebetween the in-shunt parallel L-C resonator combination and the in-shuntnon-resonant susceptance, and the in-shunt BVD model and the two in-lineadmittance inverters may be transformed into an in-line BVD model and areactance in series with the in-line BVD model.

In one embodiment, a plurality of resonant elements, a plurality ofreactive circuit elements, and a plurality of resonator models areprovided. In this case, the method may further comprise dividing theinitial filter circuit design into a plurality of sub-set circuitdesigns, each of which includes one of the resonant elements and one ormore of the plurality of reactive circuit elements, wherein, for eachsub-set circuit design, the resonant element and the reactive circuitelement(s) are transformed into a respective one of the acousticresonator models.

The method further comprises adding parasitic effects to the acousticfilter circuit design to create a pre-optimized filter circuit design,optimizing the pre-optimized filter circuit design to create a finalfilter circuit design (e.g., by inputting the pre-optimized filtercircuit design into a filter optimizer to create the final filtercircuit design), and constructing the acoustic microwave filter based onthe final filter circuit design. An optional method further comprisesperforming an element removal optimization of the pre-optimized filtercircuit design to create the final filter circuit design.

If a plurality of resonant elements are provided, the method mayoptionally comprise changing the order in which the plurality ofresonant elements in the pre-optimized filter circuit design aredisposed along a signal transmission path to create a plurality offilter solutions, computing a performance parameter for each of thefilter solutions, comparing the performance parameters to each other,and selecting one of the filter solutions as the pre-optimized circuitdesign based on the comparison of the computed performance parameters.In one method, the final circuit design comprises a plurality ofacoustic resonators, and the difference between the lowest resonantfrequency and the highest resonant frequency of the plurality ofacoustic resonators in the final filter circuit design is at least onetime, preferably at least two times, and more preferably at least threetimes, the maximum frequency separation of a single resonator in theplurality of acoustic resonators.

Other and further aspects and features of the invention will be evidentfrom reading the following detailed description of the preferredembodiments, which are intended to illustrate, not limit, the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings illustrate the design and utility of preferred embodimentsof the present invention, in which similar elements are referred to bycommon reference numerals. In order to better appreciate how theabove-recited and other advantages and objects of the present inventionsare obtained, a more particular description of the present inventionsbriefly described above will be rendered by reference to specificembodiments thereof, which are illustrated in the accompanying drawings.Understanding that these drawings depict only typical embodiments of theinvention and are not therefore to be considered limiting of its scope,the invention will be described and explained with additionalspecificity and detail through the use of the accompanying drawings inwhich:

FIG. 1 is a block diagram of a wireless telecommunications system;

FIG. 2 is a flow diagram illustrating a network synthesis technique usedto design an acoustic filter in accordance with one method of thepresent inventions;

FIG. 3 is a schematic diagram of an in-line non-resonant node filterused as the initial filter circuit structure for the network synthesistechnique of FIG. 2;

FIG. 4 is a schematic diagram of a parallel L-C resonator combination ofthe initial filter circuit structure of FIG. 3;

FIG. 5 is an equivalent circuit schematic diagram for a Butterworth-VanDyke (BVD) acoustic wave resonator model;

FIG. 6 is a sub-set circuit design taken from the initial filter circuitstructure (design) of FIG. 3 in accordance with the network synthesistechnique of FIG. 2, whereby an in-line acoustic resonator isincorporated into the initial filter circuit design of FIG. 3

FIGS. 7-9 are circuit transformations sequentially made to the sub-setcircuit design of FIG. 6 in accordance with the network synthesistechnique of FIG. 2;

FIG. 10 is another sub-set circuit design taken from the initial filtercircuit structure of FIG. 3 in accordance with the network synthesistechnique of FIG. 2;

FIGS. 11-13 are circuit transformations sequentially made to the sub-setcircuit design of FIG. 10 in accordance with the network synthesistechnique of FIG. 2, whereby an in-shunt acoustic resonator isincorporated into the initial filter circuit structure of FIG. 3;

FIG. 14 is a schematic diagram of an acoustic filter circuit designgenerated from the sub-set acoustic circuit designs of FIGS. 9 and 13 inaccordance with the network synthesis technique of FIG. 2;

FIG. 15 is a schematic diagram of a pre-optimized filter circuit designrealized from the acoustic filter circuit design of FIG. 14 inaccordance with the network synthesis technique of FIG. 2;

FIG. 16 is a table illustrating the element values of the pre-optimizedfilter circuit design of FIG. 15;

FIG. 17 is a S21 frequency response plot of the pre-optimized filtercircuit design of FIG. 15;

FIG. 18 is a schematic diagram of an optimized filter circuit designcreated by inputting the pre-optimized filter circuit design into acomputerized filter optimizer and performing an element removal designtechnique in accordance with the network synthesis technique of FIG. 2;

FIG. 19 is a table illustrating the element values of the optimizedfilter circuit design of FIG. 18;

FIG. 20 is an S21 frequency response plot of the optimized filtercircuit design of FIG. 18;

FIGS. 21a and 21b are S11 frequency response plots of the optimizedfilter circuit design of FIG. 18;

FIGS. 22-24 are circuit transformations sequentially made to the sub-setcircuit design of FIG. 10 in accordance with the network synthesistechnique of FIG. 2, whereby in-shunt acoustic resonators areincorporated into the resonant branches of the initial filter circuitdesign of FIG. 3;

FIG. 25 is a schematic diagram of an acoustic filter circuit designgenerated from the sub-set acoustic circuit design of FIG. 24 inaccordance with the network synthesis technique of FIG. 2;

FIG. 26 is a schematic diagram of another pre-optimized filter circuitdesign realized from the acoustic filter circuit structure of FIG. 25 inaccordance with the network synthesis technique of FIG. 2;

FIG. 27 is a table illustrating the element values of the pre-optimizedfilter circuit design of FIG. 26;

FIG. 28 is a S21 Band 5 frequency response plot of the filter circuitdesign of FIG. 25 after optimization;

FIG. 29 is a S21 Band 8 frequency response plot of the filter circuitdesign of FIG. 25 after optimization;

FIG. 30 is a schematic diagram of still another pre-optimized filtercircuit design generated in accordance with the network synthesistechnique of FIG. 2;

FIG. 31 is an S21 Band 5 frequency response plot of the filter circuitdesign of FIG. 30 after optimization; and

FIG. 32 is an S21 Band 8 frequency response plot of the filter circuitdesign of FIG. 30 after optimization.

FIG. 33a is an S21 Band 5 frequency response plot comparing an initiallossy polynomial solution and the final circuit design afteroptimization;

FIG. 33b is an S21 Band 8 frequency response plot comparing an initiallossy polynomial solution and the final circuit design afteroptimization;

FIG. 33c is an S21 Band 5 frequency response plot comparing an initiallossless polynomial solution and the final circuit design afteroptimization; and

FIG. 33d is an S21 Band 8 frequency response plot comparing an initiallossless polynomial solution and the final circuit design afteroptimization.

DETAILED DESCRIPTION OF THE EMBODIMENTS

The present disclosure describes a network synthesis technique fordesigning acoustic wave (AW) microwave filters (such as surface acousticwave (SAW), bulk acoustic wave (BAW), film bulk acoustic resonator(FBAR), microelectromechanical system (MEMS) filters)). This networksynthesis technique yields better performing and/or lower cost AWmicrowave filters (i.e., at frequencies greater than 500 MHz) overprevious AW microwave filter design methods. Such AW microwave filtersmay be either fixed frequency and/or tunable filters (tunable infrequency and/or bandwidth and/or input impedance and/or outputimpedance), and may be used for single band or multiple band bandpassfiltering and/or bandstop. Such AW microwave filters are advantageous inapplications that have demanding electrical and/or environmentalperformance requirements and/or severe cost/size constraints, such asthose found in the radio frequency (RF) frontends of mobilecommunications devices, including cellphones, smartphones, laptopcomputers, tablet computers, etc. or the RF frontends of fixedcommunications devices, including M2M devices, wireless base stations,satellite communications systems, etc.

Example AW microwave filters described herein (e.g. FIGS. 28-29) exhibita frequency response with a single passband and a single stopband, whichis particularly useful in telecommunication system duplexers where apassband with a closely spaced stopband is required. For example, withreference to FIG. 1, a telecommunications system 10 for use in a mobilecommunications device may include a transceiver 12 capable oftransmitting and receiving wireless signals, and a controller/processor14 capable of controlling the functions of the transceiver 12. Thetransceiver 12 generally comprises a broadband antenna 16, a duplexer 18having a transmit filter 24 and a receive filter 26, a transmitter 20coupled to the antenna 16 via the transmit filter 24 of the duplexer 18,and a receiver 22 coupled to the antenna 16 via the receive filter 26 ofthe duplexer 18.

The transmitter 20 includes an upconverter 28 configured for convertinga baseband signal provided by the controller/processor 14 to a radiofrequency (RF) signal, a variable gain amplifier (VGA) 30 configured foramplifying the RF signal, a bandpass filter 32 configured for outputtingthe RF signal at an operating frequency selected by thecontroller/processor 14, and a power amplifier 34 configured foramplifying the filtered RF signal, which is then provided to the antenna16 via the transmit filter 24 of the duplexer 18.

The receiver 22 includes a notch or stopband filter 36 configured forrejecting transmit signal interference from the RF signal input from theantenna 16 via the receiver filter 26, a low noise amplifier (LNA) 38configured for amplifying the RF signal from the stop band filter 36with a relatively low noise, a bandpass filter 40 configured foroutputting the amplified RF signal at a frequency selected by thecontroller/processor 14, and a downconverter 42 configured fordownconverting the RF signal to a baseband signal that is provided tothe controller/processor 14. Alternatively, the function of rejectingtransmit signal interference performed by the stopband filter 36 caninstead be performed by the duplexer 18. Or, the power amplifier 34 ofthe transmitter 20 can be designed to reduce the transmit signalinterference.

It should be appreciated that the block diagram illustrated in FIG. 1 isfunctional in nature, and that several functions can be performed by oneelectronic component or one function can be performed by severalelectronic components. For example, the functions performed by the upconverter 28, VGA 30, bandpass filter 40, downconverter 42, andcontroller/processor 14 are oftentimes performed by a single transceiverchip. The function of the bandpass filter 32 can be performed by thepower amplifier 34 and the transmit filter 24 of the duplexer 18.

The exemplary network synthesis technique described herein is used todesign acoustic microwave filters for the front-end of thetelecommunications system 10, and in particular the transmit filter 24of the duplexer 18, although the same technique can be used to designacoustic microwave filters for the receive filter 26 of the duplexer 18and for other RF filters.

Referring now to FIG. 2, one exemplary network synthesis technique 50for designing an AW microwave filter will be described. First, thefilter requirements, which comprise the frequency response requirements(including passband, return loss, insertion loss, rejection, linearity,noise figure, input and output impedances, etc.), as well as size andcost requirements, and environmental requirements, such as operatingtemperature range, vibration, failure rate, etc., are established by theapplication of the filter (step 52). In the illustrated embodiment, thedesign targets the following requirements: one passband from 1850 MHz to1910 MHz with a maximum insertion loss requirement of 2 dB, and threestopbands, a first one from 1930 MHz to 1990 MHz with a minimumrejection of 44 dB, a second one from 2010 MHz to 2025 MHz and a minimumrejection of 20 dB, and a third one from 2110 MHz to 2155 MHz with aminimum rejection of 45 dB.

Next, the structural types of circuit elements to be used in the AWfilter are selected; for example, the structural type of resonator (SAW,BAW, FBAR, MEMS, etc.) and the types of inductor, capacitor, and switch,along with the materials to be used to fabricate these circuit elements,including the packaging and assembly techniques for fabricating thefilter, are selected (step 54). In the particular example describedherein, the selection of circuit element types are SAW resonators andcapacitors constructed on a substrate composed of 42-degree XY-cutLiTaO3.

Then, an initial circuit structure, such as an in-linenon-resonant-node, or in-line, or in-line with cross couplings, orin-line non-resonant node with cross couplings, etc., is selected basedon the passband(s) and/or stopband(s) obtained from the frequencyresponse requirements (step 56). In the illustrated embodiment, theinitial circuit structure selected is the in-line non-resonant-nodestructure, such as those described in U.S. Pat. Nos. 7,719,382,7,639,101, 7,863,999, 7,924,114, 8,063,714, and U.S. Provisional PatentApplication Ser. No. 61/802,114, entitled “Element Removal Design inMicrowave Filters,” which are all expressly incorporated herein byreference. For the purposes of this specification, the term “structure”shall refer to the element types and their interconnections withoutconsideration the values of the elements.

Referring to FIG. 3, one such embodiment of an in-line non-resonant-nodeinitial filter circuit structure 100 generally comprises a signaltransmission path 102 having an input 104 (represented by node S) and anoutput 106 (represented by node L), a plurality of nodes 108(represented by nodes S, 1, 2 . . . n) disposed along the signaltransmission path 102, a plurality of resonant branches 110 respectivelycoupling the nodes 108 to ground, and a plurality of non-resonantbranches 112 respectively coupling the nodes 108 to ground in respectiveparallel to the resonant branches 110.

The initial filter circuit structure 100 further comprises a pluralityof in-shunt resonant elements 114 (represented by susceptances B^(R1),B^(R2) . . . B^(Rn)) respectively located in the resonant branches 110and a plurality of in-shunt non-resonant elements 116 (represented byadmittance inverters J₁₁, J₂₂ . . . J_(nn)) in series with the resonantelements 114. The initial filter circuit structure 100 further comprisesa plurality of in-shunt non-resonant elements 118, two of which couplethe node S and node L to ground (represented by susceptances B^(NS) andB^(NL) respectively) and four of which are respectively located in thenon-resonant branches 110 (represented by B^(N1), B^(N2) . . . B^(Nn)).The initial filter circuit structure 100 further comprises a pluralityof in-line non-resonant elements 120 (represented by admittanceinverters J_(S1), J₁₂, J₂₃ . . . J_(n-1, n), J_(nL)) respectivelycoupling the nodes S, 1, 2 . . . n, L together.

The initial filter circuit structure 100 may further comprise aplurality of tuning elements (not shown) for adjusting the frequenciesof the resonant elements 114 and/or values of the non-resonant elements120, and an electrical controller (not shown) configured for tuning theinitial filter circuit structure 100 to a selected narrow-band within adesired frequency range by varying selected ones of the non-resonantelements 116-120. Thus, the initial filter circuit structure 100 isuseful for network synthesis of reconfigurable bandpass filters,provided that the high Q-factor resonant elements 114 used to realizethe susceptance B^(R) values are well-described by a parallel L-Cresonator combination, i.e. tank circuit, as shown in FIG. 4.

The high Q-factor resonant elements 114 are better described using aButterworth-Van Dyke (BVD) model 122 illustrated in FIG. 5. BVD models122 may also describe SAW resonators, which may be fabricated bydisposing interdigital transducers (IDTs) on a piezoelectric substrate,such as crystalline Quartz, Lithium Niobate (LiNbO₃), Lithium Tantalate(LiTaO₃) crystals or BAW (including FBAR) resonators fabricated inmaterials such as quartz or Aluminum Nitride, or MEMS resonators. TheBVD model 122 includes a motional capacitance C_(m) 124, a staticcapacitance C₀ 126, and a motional inductance L_(m) 128. The motionalcapacitance C_(m) 124 and motional inductance L_(m) 128 may result fromthe interactions of electrical and acoustical behavior, and thus, may bereferred to as the motional arm of the BVD model 122. The staticcapacitance C₀ 126 may result from electrical behavior of the structurealone (conductors, dielectrics and gaps), and thus, may be referred toas the static (non-motional) capacitance of the BVD model 122. Theparameters are related by the following equations:

$\begin{matrix}{{\omega_{R} = \frac{1}{\sqrt{L_{m}C_{m}}}};} & \lbrack 2\rbrack \\{{\frac{\omega_{A}}{\omega_{R}} = \sqrt{1 + \frac{1}{\gamma}}},} & \lbrack 3\rbrack\end{matrix}$

where ω_(R) and ω_(A) may be the respective resonance and anti-resonancefrequencies for any given acoustic resonator, and gamma γ may depend ona material's property, which may be further defined by:

$\begin{matrix}{\frac{C_{0}}{C_{m}} = {\gamma.}} & \lbrack 4\rbrack\end{matrix}$

Typical γ values may range from about 12 to about 18 for 42-degree X Ycut LiTaO₃. The frequency separation of an acoustic resonator means thedifference between its resonant frequency and its anti-resonantfrequency. The percentage separation of an acoustic wave resonator isthe percentage frequency separation between its resonant frequency andanti-resonant frequency, and can be computed, as follows:

$\begin{matrix}{{{percentage}{\mspace{11mu} \;}{separation}} = {\sqrt{1 + \left( \frac{1}{\gamma} \right)} - 1}} & \lbrack 5\rbrack\end{matrix}$

where γ is the ratio of the static to the motional capacitance of theresonator (equation [4]), as determined by the material properties ofthe piezoelectric material and modified by the geometry of the device.

The resonant frequency ω_(R) of an acoustic resonator means thefrequency where the magnitude of the impedance reaches a local minimumand the phase of the impedance crosses zero. The anti-resonant frequencyWA of an acoustic resonator means the frequency where the magnitude ofthe impedance reaches a local maximum and the phase of the impedancecrosses zero.

It can be appreciated from equation [2] that the resonant frequency ofeach of the acoustic resonators will depend on the motional arm of theBVD model 122, whereas the filter characteristics (e.g., bandwidth) willbe strongly influenced by γ in equation [3]. The Quality factor (Q) foran acoustic resonator 122 may be an important figure of merit inacoustic filter design, relating to the loss of the element within thefilter. Q of a circuit element represents the ratio of the energy storedper cycle to the energy dissipated per cycle. The Q factor models thereal loss in each acoustic resonator, and generally more than one Qfactor may be required to describe the loss in an acoustic resonator. Qfactors may be defined as follows for the filter examples. The motionalcapacitance C_(m) 124 may have an associated Q defined as Q_(cm)=10⁸;the static capacitance C₀ 126 may have an associated Q defined asQ_(c0)=200; and motional inductance L_(m) 128 may have an associated Qdefined as Q_(Lm)=1000. (Here for simplicity the loss in the motionalresonance is lumped into the motional inductance and the motionalcapacitance is considered to be essentially loss-less.) Circuitdesigners may typically characterize SAW resonators by resonantfrequency ω_(R), static capacitance C₀, gamma γ, and Quality factorQL_(m). For commercial applications, QL_(m), may be about 1000 for SAWresonators, and about 3000 for BAW resonators.

Referring back to the FIG. 2, the frequency response requirements arethen mapped to a normalized design space (step 58). The mapping may beperformed using a suitable algorithm, such as a square-root/quadraticmapping technique (see George L. Matthaei, Microwave Filters,Impedance-Matching Networks, and Coupling Structures, McGraw-Hill BookCompany, pp. 95-97, 438-440 (1964), or a logarithmic/exponential mappingtechnique more suitable to acoustic wave resonators.

One attractive logarithmic mapping technique uses the followingequations:

$\begin{matrix}{{\Omega = {{\ln \left( \frac{\omega^{2}}{\omega_{p}^{2}} \right)}/{\ln \left( {1 + \frac{1}{\gamma}} \right)}}},} & \lbrack 6\rbrack \\{{{\Omega_{R} - \Omega_{A}}} = 1} & \lbrack 7\rbrack\end{matrix}$

where ω_(p)/2π is the geometric center frequency of the passband orstopband, ω/2π is the real frequency, Ω is the mapped frequency, γ isthe ratio of the static to the motional capacitance of the resonator,and Ω_(R) is the mapped resonant frequency of the resonator, and Ω_(A)is the mapped anti-resonant frequency of the resonator.

Next, lossless circuit response variables are provided in the form of aratio between numerator polynomials defining transmission zeroes anddenominator polynomials defining reflection zeroes multiplied by a scalefactor, as provided in equation [1] (step 60). In general, the totalnumber of transmission zeroes may be less than, equal to, or greaterthan the total number of reflection zeroes, and often one or morereflection zeroes will lie outside any passband of the filter.

Alternatively, lossy circuit response variables can be provided byincorporating a loss factor into equation [1] as follows:

$\begin{matrix}\begin{matrix}{{H(s)} = \frac{N(s)}{D(s)}} \\{{= {K\frac{\left( {s - z_{1} + \frac{i}{Q}} \right)\left( {s - z_{2} + \frac{i}{Q}} \right)\mspace{14mu} \ldots \mspace{14mu} \left( {s - z_{m - 1} + \frac{i}{Q}} \right)\left( {s - z_{m} + \frac{i}{Q}}\; \right)}{\left( {s - p_{1} + \frac{i}{Q}} \right)\left( {s - p_{2} + \frac{i}{Q}} \right)\mspace{14mu} \ldots \mspace{14mu} \left( {s - p_{n - 1} + \frac{i}{Q}} \right)\left( {s - p_{n} + \frac{i}{Q}}\; \right)}}},}\end{matrix} & \lbrack 8\rbrack\end{matrix}$

where N(s) is the numerator polynomial, D(s) is the denominatorpolynomial, the z_(i)'s are the roots (or transmission zeroes) of theequation N(s)=0, the p_(i)'s are the roots (or reflection zeroes) of theequation D(s)=0, m is the number of transmission zeroes, n is the numberof reflection zeroes, and K is a scale factor, i is the imaginary unit,and Q is the net effective quality factor of the resonators, othercircuit elements, and parasitic losses. The qualify factor Q may be thesame or may be different amongst the resonators and other circuitelements. Use of the resulting “lossy polynomial” enables a filtersynthesis design method that includes the effect of loss. Incorporatingloss into the polynomials provides an initial filter solution that iscloser to the final filter solution, thereby reducing the time andcomputation needed to design the filter.

For example, with reference to FIGS. 33a and 33b , a filter designhaving a first passband centered at 836.5 MHz (Band 5) (FIG. 33a ), anda second passband centered at 897.5 MHz (Band 8) (FIG. 33b ), can bedesigned in accordance with equation [8], assuming a net effective Q of200 for the resonators and other circuit elements forming the firstpassband, and a net effective Q of 250 for the resonators and othercircuit elements forming the second passband. Curves 80 a represent theS21 frequency responses of the filter prior to optimization, whereascurves 80 b represent the S21 frequency response of the fully optimizedfilter. As can be seen in FIGS. 33a and 33b , the curves 80 a, 80 bclosely follow each other, thereby demonstrating that the incorporationof loss into the polynomial equation provides an initial filter solutionthat closely matches the final filter solution. In contrast, and withreference to FIGS. 33c and 33d , the same filter can be designed inaccordance with equation [1], wherein no loss is taken into account(Q=0) for each resonator. Curves 80 c represent the S21 frequencyresponse prior to optimization, whereas curves 80 b again represent theS21 frequency response of the fully optimized filter. As can be seen inFIGS. 33c and 33d , the curves 80 c, 80 b substantially diverge fromeach other, thereby demonstrating that not incorporating loss into thepolynomial equation provides an initial filter solution that may notclosely match the final filter solution.

Next, the mapped and normalized circuit element values for the initialfilter circuit structure 100 are then calculated from these polynomialsusing a coupling matrix or parameter extraction methods or equivalentcircuit synthesis techniques (step 62) to create an initial losslesscircuit design. For the purposes of this specification, a “circuitdesign” shall refer to the circuit structure with consideration to thevalues of the elements making up the circuit structure.

Next, equivalent circuit transformations may then be performed to reducethe number of circuit elements, or change the type of circuit elements,the size of the circuit, or the realizability of the individual circuitelements to create an acoustic filter circuit design (step 64). Thesetransformations do not substantially change the response of the initiallossless circuit design, and may utilize equivalent circuittransformations, such as equating a J-inverter to an equivalentcapacitive or inductive PI- or T-network. For example, ashunt-resonator/two J-inverter combination may be transformed into asingle series resonator; a series-resonator/two J-inverter combinationmay be transformed into a single shunt resonator, multiple parallelcapacitances may be combined into a single capacitor, or to otherwiseeliminate capacitors negative capacitors may be removed by combiningwith positive parallel capacitors to yield a single positive capacitor,multiple series inductors may be combined into a single inductor, or tootherwise eliminate inductors negative inductors may be removed bycombining with positive series inductors to yield a single positiveinductor, or other equivalent circuit transformations may be performedto obtain a lossless circuit that may have the target circuit response,but be smaller, less costly, and/or more realizable than the initiallossless circuit design.

Significantly, although the acoustic resonant elements B^(R) are bestdescribed by the BVD model 122 illustrated in FIG. 5, a challenge arisesbecause the BVD model 122, due to its additional static capacitance C₀,cannot be directly incorporated into the L-C equivalent initial filtercircuit design 100 illustrated in FIG. 4. Thus, one particular type ofcircuit transformation involves transforming the initial filter circuitdesign 100 into a suitable structure in which an acoustic resonatormodel, and in this case a BVD model 122, can be incorporated. Thiscircuit transformation can best be performed by dividing the initialfilter circuit design 100 into multiple sub-sets equal to the number ofresonating elements 114. Each sub-set includes the circuit elements thatare coupled to each node to which a resonant branch 110 and anon-resonant branch 112 are coupled. The nature of each sub-set willdepend on whether a shunt acoustic resonator or an in-line acousticresonator is desired.

For example, in one transformation technique that incorporates anin-line acoustic resonator into the initial filter circuit design 100, aparticular subset circuit design includes a resonant element 114(susceptance B^(R)) coupled from the respective node 108 to ground, anon-resonant element 116 (admittance inverter J) coupled in series withthe resonant element 114, a non-resonant element 118 (susceptance B^(N))coupled from the respective node 108 to ground in parallel to theresonant element 114 (susceptance B^(R)), and two non-resonant elements120 (admittance inverters J) coupled in-line to the respective node 108.For example, as illustrated in FIG. 6, the sub-set 130 a includes node1, and thus, resonant element B^(R1) is coupled from the respective node108 to ground, admittance inverter element J₁₁ is coupled in series withthe resonant element B^(R1), non-resonant element B^(N1) is coupled fromthe respective node 108 to ground in parallel with the resonant elementB^(R1), and two admittance inverters J_(S1) and J₁₂ coupled in-line withthe respective node 108.

As shown in FIG. 7, the admittance inverter J₁₁ is replaced with acapacitive PI-network (capacitors −C₁₁, C₁₁, and −C₁₁), and theresonating element B₁ ^(R) is replaced with a parallel L-C resonatorcombination of an inductance (inductor L^(R1)) and a capacitance(capacitor C^(R1)). The circuit sub-structure 132 represented by thePI-network consisting of capacitors −C₁₁, C₁₁, and −C₁₁ and the parallelL-C resonator combination of the inductor L^(R1) and the capacitorC^(R1) can be transformed into a series L-C resonator combination 134 ofan inductance (inductor L^(R1′)) and capacitance (capacitor C^(R1′)).Significantly, this series L-C combination 134 can be realized by theseries resonance leg of a BVD model 122, so that it can be betterincorporated into the circuit sub-structure 132.

In order to incorporate the BVD model 122 into the circuit sub-structure132, the static capacitance C₀ of the BVD model 122 must beaccommodated. This can be accomplished by replacing the parallelsusceptance B₁ ^(N) with a capacitance (C₀ ^(R1′) and susceptanceB^(N1′)), as shown in FIG. 8. C₀ ^(R1′) represents the staticcapacitance of the BVD model 122 and B^(N1′) is given by therelationship B^(N1)−ω(C₀ ^(R1)). The susceptance B^(N1′), two in-lineadmittance inverters J_(S1) and J₁₂, and shunt acoustic resonator 122can then be transformed into an in-line acoustic resonator 122 a and aseries reactance 136 (designated X₁), as illustrated in FIG. 9.

In a transformation technique that incorporates an in-shunt acousticresonator into the initial filter circuit design 100, a particularsub-set includes a resonant element 114 (susceptance B^(R)) coupled fromthe respective node 108 to ground, a non-resonant element 116(admittance inverter J) coupled in series with the resonant element 114,and a non-resonant element 118 (susceptance B^(N)) coupled from therespective node 108 to ground in parallel to the resonant element 114(susceptance B^(R)). For example, as illustrated in FIG. 10, the sub-set130 b includes node 2, and thus, resonant element B^(R2) is coupled fromthe respective node 108 to ground, admittance inverter element J₂ iscoupled in series with the resonant element B^(R2), and non-resonantelement B^(N2) is coupled from the respective node 108 to ground inparallel with the resonant element B^(R2).

As shown in FIG. 11, the admittance inverter J₂₂ is replaced with acapacitive PI-network (capacitors −C₂₂, C₂₂, and −C₂₂), and theresonating element B^(R2) is replaced with a parallel L-C resonatorcombination of an inductance (inductor L^(R2)) and a capacitance(capacitor C^(R2)). The circuit sub-structure 132 represented by thePI-network consisting of capacitors −C₂₂, C₂₂, and −C₂₂ and the parallelL-C resonator combination of the inductor L^(R2) and the capacitorC^(R2) can be transformed into a series L-C combination 134 of aninductance (inductor L^(R2′)) and capacitance (capacitor C^(R2′)).Significantly, this series L-C combination 134 can be realized by theseries resonance leg of a BVD model 122, so that it can be betterincorporated into the circuit sub-structure 132.

In order to incorporate the BVD model 122 into the circuit sub-structure132, the static capacitance C₀ of the BVD model 122 must beaccommodated. This can be accomplished by replacing the parallelsusceptance B^(2N) with a capacitance (C₀ ^(R1′) and susceptanceB^(N1′)), as shown in FIG. 12. C₀ ^(R2′) represents the staticcapacitance of the BVD model 122 and B^(N2′) is given by therelationship B^(N2)−ω(C₀ ^(R2)). Thus, an in-shunt acoustic resonator122 b can be realized, as illustrated in FIG. 13.

It can be appreciated that the initial filter circuit design 100 can bedivided into alternating sub-sets 130 a and 130 b, such that a filtercircuit design having alternating in-line acoustic resonators 122 a andin-shunt resonators 122 b can be generated. For example, an initialfilter circuit design 100 with nine resonators B^(R) can be transformedinto an acoustic filter circuit structure 150 a having five in-lineacoustic resonators 122 a and four in-shunt acoustic resonators 122 barranged in an alternating fashion, as illustrated in FIG. 14.

Although the circuit transformation step is described as being performedon the initial filter circuit design (i.e., after calculating the mappedand normalized circuit elements values), it should be appreciated thatthe circuit transformations step can be performed on the initial filtercircuit structure (i.e., prior to calculating the mapping and normalizedcircuit element values) to create an acoustic filter circuit structure,in which case, the mapped and normalized circuit element values for theacoustic filter circuit structure can be computed to create an acousticfilter circuit design.

Referring back to FIG. 2, the circuit elements of the acoustic filtercircuit design 150 a are unmapped to a real design space (i.e., losslesscircuit elements (L's and C's) with real frequencies) in accordance withthe inverse of the mapping technique initially used to map the frequencyresponse requirements to the normalized design space (step 66). Forexample, if the logarithmic mapping technique of equation [6] was usedto map the frequency response requirements to the normalized space, thenthe following logarithmic unmapping equation can be used to unmap thenormalized circuit element values to the real design space:

$\begin{matrix}{\omega = {\omega_{p}\left( {1 + \frac{1}{\gamma}} \right)}^{\Omega/2}} & \lbrack 8\rbrack\end{matrix}$

Notably, any B value can be realized by either an L or a C depending onthe sign of B. Unmapping of the normalized circuit values yields therealized circuit shown in FIG. 15 along with the values of the resonantfrequencies ω_(R) and static capacitances C₀ for each resonator, and thecapacitances and inductances of the capacitors and inductors, as shownin FIG. 16, which when simulated, resulted in the frequency responseillustrated in FIG. 17. (Note: the inductor L1 and the capacitor C1 areadded at the end of the synthesis by pole extraction to provide equalinput and output impedance of the network.)

Next, parasitic effects are added to the acoustic filter circuit design150 a using an electromagnetic simulator, such as Sonnet® Software, andadding busbar (interconnection) losses to arrive at a pre-optimizedfilter circuit design (step 68). The losses of the acoustic resonatorsmay be included by associating a Q factor for the respective circuitelements. In this embodiment, the motional capacitance C_(m) 124 has anassociated Q defined as Q_(cm)=10⁸; the static capacitance C₀ 126 has anassociated Q defined as Q_(c0)=200; and motional inductance L_(m) 128has an associated Q defined as Q_(Lm)=1000. The remaining inductors havean associated Q defined as Q_(u)=60, and the remaining capacitors havean associated Q defined as Q_(u)=200. A busbar (interconnection)resistance of R_(S)=0.5 ohms is also added for each acoustic resonator.

The pre-optimized filter circuit design is then input into acomputerized filter optimizer to create a final filter circuit design(step 70). In an optional method, an element removal optimization (ERO)technique is implemented during the optimization, where unnecessary or“vanishing” circuit elements are removed or reduced to simpler circuitelements, resulting in the final filter circuit design illustrated inFIG. 18. The ERO technique is described in U.S. Provisional PatentApplication Ser. No. 61/802,114, entitled “Element Removal Design inMicrowave Filters,” which is expressly incorporated herein by reference.The optimization and ERO technique resulted in resonant frequenciesω_(R) and static capacitances C₀ for each resonator, and capacitances ofthe capacitors, as shown in FIG. 19, which when simulated, resulted inthe frequency response illustrated in FIG. 20, which meets the targetfrequency response requirements.

Notably, it is expected that multi-band filters designed in accordancewith the network synthesis technique illustrated in FIG. 2 will haveresonances and resonators with resonant frequencies spanning ranges thatare relatively large in contrast to microwave acoustic filters designedin accordance with prior art image design techniques and simpleextensions thereof.

For example, one measure to which the span of resonance frequencies of afilter or its resonators can be compared is the frequency separation ofthe resonator in the filter with the highest resonant frequency. For a42-degree XY-cut LiTaO₃ substrate, γ is greater than about 12. Anyparasitic capacitance from the realization of the acoustic resonator mayincrease the γ and therefore decrease the percentage separation, whileparasitic inductance may effectively decrease γ. In this example, forγ=12, the percentage separation is 4.0833%, and therefore, theseparation of the resonator with the highest resonant frequency is about88.1 MHz (i.e., a resonant frequency of 2151.57 MHz times the percentseparation of 4.0833%). Another measure to which the span of resonancefrequencies of a filter or its resonators can be compared is the averagefrequency separation of its resonators, in this case 77.32 MHz.

In contrast to the frequency separation of an acoustic resonator, the“frequency difference” between two acoustic resonators means theabsolute frequency difference between the resonant frequencies of thetwo resonators, and the frequency difference between two resonances of afilter is the absolute frequency difference between the two resonances.FIGS. 21(a) and 21(b) show the return loss (S11) of the filter definedin FIGS. 18-19. Return loss minima correspond to resonances of thefilter circuit and also correspond to reflection zeroes of the initialfilter design. FIG. 21(a) shows the resonances of the filter primarilyresponsible for forming the filter passband, N1 through N7. Thefrequency difference between the highest and lowest resonance shown inFIG. 21(a) is 102 MHz or about 1.32 times the average frequencyseparation of the resonators. In addition, the frequency differencebetween the highest and lowest resonance of the combined FIGS. 21(a) and21(b) is 349 MHz (2173-1824 MHz), or about 4.51 times the averagefrequency separation of the resonators, while the frequency differencebetween the highest and lowest frequency resonators in the filter is459.37 MHz (2151.57-1892.2 MHz), or about 5.94 times the averagefrequency separation of the resonators.

Thus, it is expected that the difference between the lowest resonancefrequency and the highest resonance frequency of the passband resonancesin the final filter circuit design will be at least 1.25 times theaverage separation of the resonators.

It is expected that multi-band filters designed in accordance with thenetwork synthesis technique illustrated in FIG. 2 will have resonatorsas well as resonances corresponding to reflection zeroes that arelocated relatively far from the passband in contrast to filters designedin accordance with prior art image design techniques, wherein theresonators and resonances corresponding to reflection zeroes areconfined to the passband or very close to it.

In particular, resonances corresponding to reflection zeroes occur atfrequencies where the local return loss (and/or S11) minima and localinsertion loss (and/or S21) maxima coincide to within less than aboutfive percent of the maximum frequency separation—less than about 4.405MHz for this example. Alternatively, resonances corresponding toreflection zeroes occur at local minima and at local maxima of the delayof S11 (not shown). As can be seen from FIG. 21b , some resonancescorresponding to reflection zeroes (in particular, the resonancescorresponding to markers N1, N2, and N6-N9) are located outside and farfrom the passband (1850 MHz to 1910 MHz). The frequency differencebetween a resonance corresponding to a reflection zero and the nearestpassband edge may be greater than once, perhaps greater than 1.25 times,and perhaps greater than twice, the maximum frequency separation (about88.1 MHz in this example). In this particular example, reflection zeroesare located up to 3.40 times the average resonator separation (77.32MHz) from the edge of the passband. Relative to the passband width (60MHz), reflection zeroes N1, N2 are 43.33% and 28.33% below the loweredge of the passband, and reflection zeroes N6, N7 are 13.33% and 26.67%above the upper edge of the passband. Reflection zeroes N1, N2, N6, andN7 are contiguous with each other. Reflection zeroes N8, N9, which arenot contiguous with the passband reflection zeroes N1, N2, N6, N7, are311.67% and 438.33% above the upper edge of the passband. The insertionloss of the final filter circuit design is preferably less than 3 dB,and more preferably less than 2 dB.

Referring back to FIG. 2, once the final filter circuit design isachieved, an actual microwave filter is constructed based on the finalfilter circuit design (step 72). Preferably, the circuit element valuesof the actual microwave filter will match the corresponding circuitelement values in the final filter circuit design.

Notably, a survey of different frequency responses may be analyzed andcompared at various points in the network synthesis technique 50. In oneembodiment, a survey of different frequency responses may be analyzedand compared based on different versions of the acoustic filter circuitdesign 150 a generated at step 68 to arrive at a pre-optimized circuitdesign that is input into the computerized filter optimizer to createthe final filter circuit design at step 70. For example, differentacoustic resonator frequency orderings between input and output may beperformed. In particular, the order in which the acoustic resonators aredisposed along the signal transmission path may be changed to createmultiple filter solutions, one or more performance parameters may becomputed for each of the filter solutions, the performance(s) parametersfor the different filter solutions can be compared to each other, andthe best filter solution (and thus, ordering of the resonators) may beselected based on this comparison. This survey process may address allpossible permutations of the ordering of the acoustic resonatorfrequencies in the real filter circuit design. The performanceparameters may be, e.g., one or more of an insertion loss, return loss,rejection, group delay, node voltages, branch currents, either atspecific or multiple frequencies in order to evaluate each circuitresponse against desired performance characteristics in the filterrequirement. The survey process may yield quantitative or qualitativeperformance metric values indicating how a specific circuit may performversus the filter requirement.

In other embodiments, the survey process may also address all realizablevalues of the static capacitances C₀ of the resonators, all permutationsof positive (inductive) and or negative (capacitive) values (parities)of J-inverters, and other parameters that may be varied in the losslessdesign that may not change its response function, but may change theresponse of a realizable low-loss circuit. Further details discussing asurvey process that reorders resonant frequencies is disclosed in U.S.Pat. No. 7,924,114, entitled “Electrical Filters with ImprovedIntermodulation Distortion,” which is expressly incorporated herein byreference.

Although the filter requirements have been described in this embodimentas defining fixed passbands and stopbands, it should be appreciated thatthe filter requirements can define multiple reconfigurable passbandsand/or stopband. For example, in one embodiment, the design may bereconfigurable between two states: a first state (called Band 5) thatpasses frequencies between 824 MHz and 849 MHz with less than 3.5 dBinsertion loss and rejects frequencies between 869 MHz and 894 MHz by atleast 40 dB; and a second state (called Band 8) that passes frequenciesbetween 880 MHz and 915 MHz with less than 3.5 dB insertion loss andrejects frequencies between 925 MHz and 960 MHz by at least 40 dB (step52). The circuit element type is selected as SAW resonators constructedon 15-degree Y-cut LiTaO3 substrates and capacitors integrated onto the15-degree Y-cut LiTaO3 substrate (step 54).

Then, the initial filter circuit structure 100 illustrated in FIG. 3 isselected based on the passband(s) and/or stopband(s) obtained from thefrequency response requirements (step 56). In this case, the number ofresonators is six. Then, the frequency requirements are mapped intonormalized space (step 58), a lossless circuit response is selected inthe form of a polynomial ratio (step 60), and the mapped and normalizedcircuit element values in the initial filter circuit structure 100 arethen calculated from these polynomials using a coupling matrix orparameter extraction methods or equivalent circuit synthesis techniquesto create an initial filter circuit design (step 62).

Next, equivalent circuit transformations are performed on the initialfilter circuit design 100 to accommodate acoustic resonators (step 64).In the same manner described above, the circuit transformation dividesthe initial filter circuit design 100 into multiple sub-set circuitdesigns equal to the number of resonating elements 114 (in this case,six), resulting in six shunt acoustic resonators.

In one transformation technique that incorporates an in-shunt acousticresonator into the initial filter circuit design 100, the sub-set 130illustrated in FIG. 6 can be transformed by replacing the admittanceinverter J_(S1) with a capacitive PI-network (capacitors −C_(S1),C_(S1), and −C_(S2)), the admittance inverter J₁₂ with a capacitivePI-network (capacitors −C₁₂, C₁₂, and −C₁₂), the admittance inverter J₁₁with a capacitive PI-network (capacitors −C₁₁, C₁₁, and −C₁₁), and theresonating element B₁ ^(R) with a parallel L-C resonator combination ofan inductance (inductor L^(R1)) and a capacitance (capacitor C^(R1)), asillustrated in FIG. 22. In the same manner described above with respectto FIG. 7, the circuit sub-structure 132 represented by the PI-networkconsisting of capacitors −C₁₁, C₁₁, and −C₁₁ and the parallel L-Cresonator combination of the inductor L^(R1) and the capacitor C^(R1)can be transformed into a series L-C combination 134 of an inductance(inductor L^(R1′)) and capacitance (capacitor C^(R1′)). In order toaccommodate the static capacitance C₀ of the BVD model 122, the threeadjacent parallel capacitances and susceptances (−C_(S1), −C₁₂, and B₁^(N)) are replaced with a capacitance (C₀ ^(R1′) and susceptance B₁^(N′)), as shown in FIG. 23. C₀ ^(R1′) represents the static capacitanceof the BVD model 122 and B^(N1′) is given by the relationshipB^(N1)−ω(C_(S1)+C₁₂+C₀ ^(R1)). Thus, an in-shunt acoustic resonator 122can be realized, as illustrated in FIG. 24. The other sub-sets 130 ofthe initial filter circuit design 100 can be transformed in the samemanner to arrive at an acoustic filter circuit structure 150 b havingsix in-shunt acoustic resonators 122, as illustrated in FIG. 25.

The circuit elements of the acoustic filter circuit structure 150 b arethen unmapped into real space (step 66), and parasitic effects are addedto the acoustic filter circuit structure 150 b to arrive at apre-optimized circuit design (step 68). As discussed above, the lossesof the circuit elements may be included by associating a Q factor forthe respective circuit elements. In this embodiment, the motionalcapacitance C_(m) to has an associated Q defined as Q_(cm)=10⁸; thestatic capacitance C₀ has an associated Q defined as Q_(c0)=140; andmotional inductance L_(m) has an associated Q defined as Q_(Lm)=3000.The remaining inductors have an associated Q defined as Q_(u)=60, andthe remaining capacitors have an associated Q defined as Q_(u)=200. Abusbar (interconnection) resistance of R_(S)=0.5 ohms is also added foreach acoustic resonator. In this embodiment, switch parasitics of 3pF/(mm gate width) and 1.0 Ohm*(mm gate width) are also added.

Next, the pre-optimized filter circuit design is input into a computerfilter optimizer with the optional ERO technique to create a finalcircuit design (step 70). Prior to optimization, switches are added toeach branch where the impedance is different between the two bands,thus, creating a single circuit from the two separate designs to beoptimized, as illustrated in FIG. 26. The gate width of each switch,value of an inductor or capacitor (if needed), and the circuitconfiguration of the branch is selected, so that the impedance of agiven branch will be the required band 5 impedance in one switch stateand the required band 8 impedance in the other switch state. The EROtechnique is then repeated on the combined circuit. The optimizationprocess yields the resonant frequencies o)_(R) and static capacitancesC₀ for each resonator, and the capacitances and inductances of thecapacitors and inductors, as shown in FIG. 27, which when simulated,resulted in the frequency response for band 5 illustrated in FIG. 28 andthe frequency response for band 8 illustrated in FIG. 29.

As previously discussed, a survey of different frequency responses maybe analyzed and compared at various points in the network synthesistechnique 50. In one embodiment, a survey of different frequencyresponses may be analyzed and compared based on different versions ofthe acoustic filter circuit design 150 a generated at step 68 to arriveat a pre-optimized circuit design that is input into the computerizedfilter optimizer to create the final filter circuit design at step 70.For example, pairs of circuits (one band 5 and one band 8) are producedwith each possible ordering of resonator frequencies, each possibleparity of the J inverters (inductor or capacitive), and a selection ofstatic capacitance C₀ values for the resonators. In this survey process,all possible permutations of resonator frequency orderings, all possibleparities, a range of practical static capacitance C₀ values of 0.95,1.9, 3.8, and 7.6 pF are used to calculate insertion loss at thepassband center frequency for each design. One pair of designs (one band5 and one band 8 with the same resonator order and static capacitance C₀values) may then be selected.

Although the previous embodiment includes passbands and/or stopbandsthat are dynamically reconfigurable, it should be appreciated that afilter constructed in accordance with the network synthesis techniquecan have fixed passbands and/or stopbands that are reconfigurable priorto final completion of the filter, but be fixed after completion of thefilter. For example, in one embodiment illustrated in FIG. 30, alossless circuit model can be realized to create a filter having eithera passband centered at either 836.5 MHz (Band 5) or 897.5 MHz (Band 8).This lossless circuit has been created by transforming the initialfilter circuit design 100 illustrated in FIG. 3 using three SAWresonators.

In a transformation technique that incorporates three in-shunt acousticresonators into the initial filter circuit design 100, thetransformation technique illustrated in FIGS. 10-13 can be utilized totransform circuit sub-sets (each including a resonant element 114(susceptance B^(R)) coupled from the respective node 108 to ground, anon-resonant element 116 (admittance inverter J) coupled in series withthe resonant element 114, and a non-resonant element 118 (susceptanceB^(N)) coupled from the respective node 108 to ground in parallel to theresonant element 114 (susceptance B^(R))) into three in-shunt acousticresonators. The circuit element type is selected as SAW resonatorsconstructed on 42-degree Y-cut LiTaO₃ substrates and capacitorsintegrated onto the 42-degree Y-cut LiTaO3 substrate.

The filter can be reconfigured prior to completion by altering thevalues of the series elements between the resonators (in this case,C_(S1), C₁₂, C₂₃, C_(3L)) and the non-resonant shunt elements (in thiscase, L_(S), L₁, L₂, L₃, L_(L)). The filter can then be constructedusing either the values of the non-resonant elements for Band 5 or thevalues of the non-resonant elements for Band 8. The optimization processyields the static capacitances C₀ for each resonator, and thecapacitances and inductances of the capacitors and inductors, as shownin FIG. 30, which when simulated, resulted in the frequency response forband 5 illustrated in FIG. 31 and the frequency response for band 8illustrated in FIG. 32.

Computer implemented software, systems, and microwave filters designedin accordance with the method are also included. Any suitable form ofserver, computer or processor may be used to implement the method.Associated memory may be used to store the software used in associationwith the server, computer or processor.

Although particular embodiments of the present invention have been shownand described, it should be understood that the above discussion is notintended to limit the present invention to these embodiments. It will beobvious to those skilled in the art that various changes andmodifications may be made without departing from the spirit and scope ofthe present invention. For example, the present invention hasapplications well beyond filters with a single input and output, andparticular embodiments of the present invention may be used to formduplexers, multiplexers, channelizers, reactive switches, etc., wherelow-loss selective circuits may be used. Thus, the present invention isintended to cover alternatives, modifications, and equivalents that mayfall within the spirit and scope of the present invention as defined bythe claims.

What is claimed is:
 1. A multi-band acoustic wave microwave filter,comprising: a signal transmission path having an input and an output; aplurality of nodes disposed along the signal transmission path; aplurality of non-resonant branches respectively coupling one or morenodes to ground, wherein each non-resonant branch comprises at least onenon-resonant element; and a plurality of resonant branches that coupleone or more nodes to ground and comprise a plurality of resonatorsdisposed on said branches, wherein the plurality of resonators define afirst band and at least one additional band and further wherein thedifference between the lowest resonant frequency and the highestresonant frequency of the first band is at least 1.25 times the averageseparation of the resonators.
 2. The multi-band acoustic wave microwavefilter according to claim 1, wherein the filter comprises one of asurface acoustic wave filter, a bulk acoustic wave filter, a bulkacoustic wave filter and a microelectromechanical filter.
 3. Themulti-band acoustic wave microwave filter according to claim 1, whereinthe filter comprises alternating in-line acoustic resonators andin-shunt resonators.
 4. The multi-band acoustic wave microwave filteraccording to claim 1, wherein the first band comprises a passband andthe at least one additional band comprises a stop band.
 5. Themulti-band acoustic wave microwave filter according to claim 1, whereinthe first band comprises a passband that exhibits a frequency responsein the range of 500-3500 MHz.
 6. The multi-band acoustic wave microwavefilter according to claim 1, further comprising at least one reactivecircuit element.
 7. The multi-band acoustic wave microwave filteraccording to claim 6, wherein the at least one reactive circuit elementcomprises a capacitor.
 8. The multi-band acoustic wave microwave filteraccording to claim 1, wherein the filter is in communication with atleast one of a duplexer and an amplifier.
 9. An RF front end circuitcomprising: at least one duplexer; at least one amplifier; and at leastone multi-band acoustic wave microwave filter comprising: a signaltransmission path having an input and an output; a plurality of nodesdisposed along the signal transmission path; a plurality of non-resonantbranches respectively coupling one or more nodes to ground, wherein eachnon-resonant branch comprises at least one non-resonant element; and aplurality of resonant branches that couple one or more nodes to groundand comprise a plurality of resonators disposed on said branches,wherein a plurality of resonators are disposed on the plurality ofresonant branches and further wherein the plurality of resonators definea first band and at least one additional band and further wherein thedifference between the lowest resonant frequency and the highestresonant frequency of the first band is at least 1.25 times the averageseparation of the resonators.
 10. An RF front end circuit according toclaim 9, wherein the filter comprises one of a surface acoustic wavefilter, a bulk acoustic wave filter, a bulk acoustic wave filter and amicroelectromechanical filter.
 11. An RF front end circuit according toclaim 9, wherein the filter comprises alternating in-line acousticresonators and in-shunt resonators.
 12. An RF front end circuitaccording to claim 9, wherein the first band of the filter comprises apassband and the at least one additional band comprises a stop band. 13.An RF front end circuit according to claim 9, wherein the first band ofthe filter comprises a passband that exhibits a frequency response inthe range of 500-3500 MHz.
 14. An RF front end circuit according toclaim 9, wherein the filter comprises at least one reactive circuitelement.
 15. An RF front end circuit according to claim 14, wherein theat least one reactive circuit element comprises a capacitor.
 16. An RFfront end circuit according to claim 9, wherein the filter is incommunication with at least one of a duplexer and an amplifier.
 17. Themulti-band acoustic wave microwave filter according to claim 1, whereinthe first band and the at least one additional band are both passbands.18. An RF front end circuit according to claim 9, wherein the first bandand the at least one additional band are both passbands.